A new estimation procedure for a partially nonlinear model via a mixed‐effects approach

The authors consider the estimation of the parametric component of a partially nonlinear semiparametric regression model whose nonparametric component is viewed as a nuisance parameter. They show how estimation can proceed through a nonlinear mixed‐effects model approach. They prove that under certain regularity conditions, the proposed estimate is consistent and asymptotically Gaussian. They investigate its finite‐sample properties through simulations and illustrate its use with data on the relation between the photosynthetically active radiation and the net ecosystem‐atmosphere exchange of carbon dioxide.     

Estimation of the Force of Infection from Current Status Data Using Generalized Linear Mixed Models

Based on sero-prevalence data of rubella, mumps in the UK and varicella in Belgium, we show how the force of infection, the age-specific rate at which susceptible individuals contract infection, can be estimated using generalized linear mixed models (McCulloch & Searle, 2001). Modelling the dependency of the force of infection on age by penalized splines, which involve fixed and random effects, allows us to use generalized linear mixed models techniques to estimate both the cumulative probability of being infected before a given age and the force of infection. Moreover, these models permit an automatic selection of the smoothing parameter. The smoothness of the estimated force of infection can be influenced by the number of knots and the degree of the penalized spline used. To determine these, a different number of knots and different degrees are used and the results are compared to establish this sensitivity. Simulations with a different number of knots and polynomial spline bases of different degrees suggest - for estimating the force of infection from serological data - the use of a quadratic penalized spline based on about 10 knots.     

Saddlepoint Approximation for Sample and Bootstrap Quantiles

The paper gives the saddlepoint approximation for the distribution function of the sample quantile. A comparison of the saddlepoint approximations for the distribution functions of the sample quantile and the bootstrap quantile shows that the error of the bootstrap approximation to the distribution of the sample quantile obtained by Singh (1981) as an absolute error is actually a relative error.     

Subsampling Variance Estimation for Non-stationary Spatial Lattice Data

ABSTRACT.  Most proposed subsampling and resampling methods in the literature assume stationary data. In many empirical applications, however, the hypothesis of stationarity can easily be rejected. In this paper, we demonstrate that moment and variance estimators based on the subsampling methodology can also be employed for different types of non-stationarity data. Consistency of estimators are demonstrated under mild moment and mixing conditions. Rates of convergence are provided, giving guidance for the appropriate choice of subshape size. Results from a small simulation study on finite-sample properties are also reported.     

Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment

Standard methods of estimation for autoregressive models are known to be biased in finite samples, which has implications for estimation, hypothesis testing, confidence interval construction and forecasting. Three methods of bias reduction are considered here: first-order bias correction, FOBC, where the total bias is approximated by the O(T^-1) bias; bootstrapping; and recursive mean adjustment, RMA. In addition, we show how first-order bias correction is related to linear bias correction. The practically important case where the AR model includes an unknown linear trend is considered in detail. The fidelity of nominal to actual coverage of confidence intervals is also assessed. A simulation study covers the AR(1) model and a number of extensions based on the empirical AR(p) models fitted by Nelson & Plosser (1982). Overall, which method dominates depends on the criterion adopted: bootstrapping tends to be the best at reducing bias, recursive mean adjustment is best at reducing mean squared error, whilst FOBC does particularly well in maintaining the fidelity of confidence intervals.     

读《唐会要》札记一则

在检阅四库本《唐会要》卷七十四《选部上.论选事》和中华本《唐会要》卷七十六《贡举中.进士》时,发现二书或整段内容此有彼无,或史事时间序次歧互淆乱,或人名和官名互有出入,或文字衍脱讹误,凡此类可拾掇的问题不在少数。     

Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring

In reliability analysis, accelerated life-testing allows for gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the simple step-stress model under Type-II censoring when the lifetime distributions of the different risk factors are independently exponentially distributed. Under this setup, we derive the maximum likelihood estimators (MLEs) of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. The exact distributions of the MLEs of the parameters are then derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions and the parametric bootstrap method, we discuss the construction of confidence intervals for the parameters and assess their performance through Monte Carlo simulations. Finally, we illustrate the methods of inference discussed here with an example.     

非线性混合整数规划的罚函数解法

主要对非线性混合整规划问题的求解进行探讨。利用罚函数把非线性混合整规划问题转化为等价的非线性规划问题,从而可通过求解一个无约束线性规划问题而得到原问题的最优解。     

Analysis of growth curve data by using cubic smoothing splines

Longitudinal data frequently arises in various fields of applied sciences where individuals are measured according to some ordered variable, e.g. time. A common approach used to model such data is based on the mixed models for repeated measures. This model provides an eminently flexible approach to modeling of a wide range of mean and covariance structures. However, such models are forced into a rigidly defined class of mathematical formulas which may not be well supported by the data within the whole sequence of observations. A possible non-parametric alternative is a cubic smoothing spline, which is highly flexible and has useful smoothing properties. It can be shown that under normality assumption, the solution of the penalized log-likelihood equation is the cubic smoothing spline, and this solution can be further expressed as a solution of the linear mixed model. It is shown here how cubic smoothing splines can be easily used in the analysis of complete and balanced data. Analysis can be greatly simplified by using the unweighted estimator studied in the paper. It is shown that if the covariance structure of random errors belong to certain class of matrices, the unweighted estimator is the solution to the penalized log-likelihood function. This result is new in smoothing spline context and it is not only confined to growth curve settings. The connection to mixed models is used in developing a rough testing of group profiles. Numerical examples are presented to illustrate the techniques proposed.     

我国混业经营条件下金融监管制度的缺陷及对策

随着全球经济一体化,混业经营体制逐步成为国际金融业的主流。我国现行金融监管体制缺乏规范的、限制性的金融集团内部交易的风险传播的制度;缺乏规范的信息披露制度;缺乏规范的市场性原则与约束。在激烈的竞争中,我们应协调好各有关监管部门之间的关系;通过合理分工,改进和加大联合监管力度,提高综合监管水平和效率;完善金融业经营监管方面的法律法规,为金融业的良性运作提供强有力的法律保障;逐步建立健全、完善的金融市场。